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A216169
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Composite numbers > 9 which yield a prime whenever a 0 is inserted between any two digits.
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13
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49, 119, 121, 133, 161, 169, 203, 253, 299, 301, 319, 323, 403, 407, 473, 493, 511, 539, 551, 581, 611, 667, 679, 713, 869, 901, 913, 943, 1007, 1067, 1079, 1099, 1211, 1273, 1691, 1729, 1799, 1909, 2021, 2047, 2101, 2117, 2359, 2407, 2533, 2717, 2759, 2899
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2359 is not prime but 23509, 23059 and 20359 are all primes.
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MAPLE
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local a, b, c, i, n, ok;
for n from 10 to q do
if not isprime(n) then
a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;
for i from 1 to b-1 do c:=a+9*10^i*trunc(a/10^i)+10^i*x;
if not isprime(c) then ok:=0; break; fi; od;
if ok=1 then print(n); fi;
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MATHEMATICA
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Select[Range[10, 3000], CompositeQ[#]&&AllTrue[Table[FromDigits[ Insert[ IntegerDigits[ #], 0, n]], {n, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2018 *)
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PROG
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(PARI) is(n, L=logint(n+!n, 10)+1, P)={!isprime(n) && !for(k=1, L-1, isprime([10*P=10^(L-k), 1]*divrem(n, P))||return) && n>9} \\ M. F. Hasler, May 10 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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